Question

The boolean expression for the output 'F' of the logic circuit shown in the figure below is

• A. $\overline{X}Y+\overline{X}.\overline{Y}+\overline{Z}$
• B. $\overline{X}Y+X\overline{Y}+Z$
• C. $XY+\overline{X}.\overline{Y}+\overline{Z}$
• D. $\overline{X}Y+X\overline{Y}+\overline{Z}$

Answer 1

The correct option is D $\overline{X}Y+X\overline{Y}+\overline{Z}$

$F=\overline{(X⨀Y)Z}=\overline{(XY+\overline{X}.\overline{Y})Z}$

$F=\overline{(XY+\overline{X}.\overline{Y})}+\overline{Z}=\overline{\left(XY\right)}\left(\overline{\overline{X}.\overline{Y}}\right)+\overline{Z}$

$F=(\overline{X}+\overline{Y})(X+Y)+\overline{Z}=\overline{X}Y+X\overline{Y}+\overline{Z}$